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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 903–912

Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas

Vadim A. Markel, Joseph A. O’Sullivan, and John C. Schotland  »View Author Affiliations


JOSA A, Vol. 20, Issue 5, pp. 903-912 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000903


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Abstract

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.

© 2003 Optical Society of America

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.6960) Medical optics and biotechnology : Tomography

History
Original Manuscript: August 2, 2002
Revised Manuscript: December 2, 2002
Manuscript Accepted: December 2, 2002
Published: May 1, 2003

Citation
Vadim A. Markel, Joseph A. O’Sullivan, and John C. Schotland, "Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas," J. Opt. Soc. Am. A 20, 903-912 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-903


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References

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